The tough tactics employed by Sassaman's battalion had their effect. Attacks in the Sunni villages like Abu Hishma, wrapped in barbed wire, dropped sharply. And his men succeeded in retaking Samarra. Winning the long-term allegiance of the Iraqis in those areas was another matter, however. If many Iraqis in the Sunni Triangle were ever open to the American project - the Shiite cities like Balad excepted - very few of them are anymore. Majool Saadi Muhammad, 49, a tribal leader in Abu Hishma, said that he had harbored no strong feelings about the Americans when they arrived in April 2003 and was proud to have three sons serving in the new American-backed Iraqi Army. Then the raids began, and many of Abu Hishma's young men were led away in hoods and cuffs. In early 2004, he said, Sassaman led a raid on his house, kicking in the doors and leaving the place a shambles. "There is no explanation except to humiliate," Muhammad told me. "I really hate them."

In retrospect, it is not clear what strategy, if any, would have won over Sunni towns like Samarra and Abu Hishma. Crack down, and the Iraqis grew resentful; ease up, and the insurgents came on strong. As Sassaman pointed out, the Americans poured $7 million of reconstruction money into Samarra, and even today, the town is not completely under American control.

But there is another reason American commanders shy from using violence on civilians: the effects it has on their own men. Pittard, the American commander in Baquba, says that he was careful not to give his men too much leeway in using nonlethal force. It wasn't just that he regarded harsh tactics as self-defeating. He feared his men could get out of control. "We were not into reprisals," Pittard says. "It's a fine line. If you are not careful, your discipline will break down."

In most of the 20th century's guerrilla wars, the armies of the countries battling the insurgents have suffered serious breakdowns in discipline. This was true of the Americans in Vietnam, the French in Algeria and the Soviets in Afghanistan. Martin van Creveld, a historian at Hebrew University of Jerusalem, says that soldiers in the dominant army often became demoralized by the frustrations of trying to defeat guerrillas. Nearly every major counterinsurgency in the 20th century failed. "The soldiers fighting the insurgents became demoralized because they were the strong fighting the weak," van Creveld says. "Everything they did seemed to be wrong. If they let the weaker army kill them, they were idiots. If they attacked the smaller army, they were seen as killers. The effect, in nearly every case, is demoralization and breakdowns of discipline."